Noncontact tracing control devices are known in which, while an optical distance detector mounted to a tracer head Is moved along a model surface, a distance to the model surface is detected in a noncontact fashion, and the operation of a machine tool is controlled in accordance with the result of distance detection representing the model shape. This type of control device is advantageous in that the model surface is not damaged when the model surface is traced. If the ankle of inclination of the model surface is large, however, the measurement axis of the optical distance detector becomes almost parallel to the model surface, and the spot on the model surface is enlarged to an ellipsoid, thus lowering the tracing accuracy. Particularly when using a trigonometric type distance detector, measurement sometimes becomes impossible due to an interference between the optical axis and the model surface.